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If the nth term of a progression be a linear expression in n, then prove that this progression is an AP - Mathematics

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Sum

If the nth term of a progression be a linear expression in n, then prove that this progression is an AP

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Solution

Let the nth term of a given progression be given by Tn = an + b, where a and b are constants.

Then, Tn-1 = a(n – 1) + b = [(an + b) – a]

∴ (Tn – Tn-1 ) = (an + b) – [(an + b) – a] = a,

which is a constant.

Hence, the given progression is an AP

Concept: Arithmetic Progression
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